In magnetic resonance imaging (MRI), a sample (e.g., a human subject) is placed in a powerful magnetic field. In the magnetic field, the hydrogen protons in the sample will align with the magnetic field in one direction or the other. The MRI machine applies a radio pulse configured specifically to affect hydrogen. The radio pulse causes the protons in a region of interest to absorb energy and spin in a different direction and at a particular frequency. At same time, or approximately the same time, gradient fields are turned on and off very rapidly in a specific manner, which alter the main magnetic field on a local level. When the radio pulse is turned off, the hydrogen protons begin to return to their natural alignment within the magnetic field and release their excess stored energy in form of radio waves. The radio waves are then detected by one or more receiver coils. The data that is collected by the receiver coils is in the form of spatial frequencies, in what is called “k-space” of the image. Frequency data in k-space can be mathematically converted to a recognizable image in the so-called image domain using a number of procedures, including for example a Fourier transform. Reconstructions of images of the sample (e.g., a human subject's brain or heart) take into account information about the orientations of applied magnetic fields and the orientations of the receiver coils.
Despite numerous advances in the field, one drawback of MRI has been the slow rate at which data is collected, such that long scanning times may be required. Subjects may be unable to remain sufficiently still for the amount of time required to obtain an image, and blurring artifacts from motion can arise which degrade the quality of the MR images.
Parallel MRI (pMRI) is a method that has been developed to address this problem. pMRI uses multiple detector coils and has each coil collect less data, thus allowing for faster scanning times. Parallel MRI uses an array of RF receiver surface coils to simultaneously (or near-simultaneously) acquire multiple sets of under-sampled k-space data. While this technique allows faster scanning of the sample, the under-sampled data that is collected has a reduced signal-to-noise ratio (SNR). The k-space data collected using pMRI is a complex combination of the actual sample data modified by the relative sensitivities of each receiver coil.
Accordingly, parallel imaging using phased array coils has been used clinically to accelerate MR data acquisition speed. Higher data acquisition rates can be achievable by using coils with more data channels. Massive array coils with a large number of data channels have been studied and developed. As a result, the data acquisition times can be reduced at the expense of reconstruction time following data acquisition. As such massive array coils become commercially available, the greatly increased computational time has become a concern to reconstruct MR images from reduced acquisitions with multiple receivers.
A number of techniques, operating in either k-space or the image domain, have been proposed for reconstructing a complete MR image from under-sampled data. Among the commercial reconstruction methods, GRAPPA is used as one of the auto-calibrated reconstruction techniques. GRAPPA reconstructs missing k-space data for each channel (known as the target channel) by a linear combination of some acquired data from all channels (source channels), where the coefficients for the linear combination are estimated using additionally acquired auto-calibration signal (ACS) lines. In conventional GRAPPA, both the number of source channels and the number of target channels are equal to the number of physical channels of the coil. Because of such channel-by-channel calculation, the computation time of GRAPPA increases almost quadratically with the number of channels. Therefore, GRAPPA causes long reconstruction times when massive array coils are used. Other auto-calibrated reconstruction methods, like SPIRiT, suffer from the same disadvantages. This leads to difficulties in real-time and high-throughput imaging.
Some attempts have been made to address this issue by reducing the effective number of channels using hardware-based or software-based approaches. In the hardware-based approach, an inline hardware RF signal combiner is used after pre-amplification and before the receiver system. This effectively constructs an eigencoil array based on the noise covariance of the receiver array. Optimal SNR and similar reconstruction qualities can be achieved using such a channel reduction. However, the required hardware can be cumbersome and expensive.
In contrast, software-based channel reduction methods are more flexible. Software coil compression processes generate a new set of fewer virtual channels that can be expressed as linear combinations of the physical channels. These methods aim at reducing the effective number of channels used for reconstruction by combining the physically acquired data from a large number of channels before image reconstruction. For example, principal component analysis (PCA) has been used to find the correlation among physical channels and reduce the number of channels to fewer effective ones by linearly combining the data from physical channels. These fewer combined channels are used for reconstruction, which leads to reduced reconstruction time. A major limitation of PCA is its computation complexity. Performing a PCA requires an order of N3 multiplications, with N being the original dimension, which becomes prohibitive when dealing with a large data set as found in modern pMRI systems.